Most of the challenged books I've reviewed on this blog fall into neither of these categories. That is, they are neither obscene for everyone nor obscene for a minor. While parents may find some of those books objectionable for any of a long list of reasons, they're mostly kidding themselves if they think the library is breaking the law by letting their kids read them.
There are some exceptions, though. The graphic novel Block Dossier, for example, might meet the definition of "obscene for minors" in some states. This is the book that resulted in the firing of two desk attendants who deleted an 11-year-old's hold on the book, in Jessamine County, Kentucky. While the book is protected speech for adults, it might be legal, in some states, to impose restrictions on a child's access to it.
I say in some states because the laws defining and regulating materials that are "harmful to minors" exist mostly at the state level, and no two states are exactly alike in this regard. While all the state laws I looked at contain some variation of the three-pronged Miller test for defining obscenity, each state uses slightly different language, casts a broader or narrower net, imposes different penalties, and permits different exemptions or exceptions.
It is the exemptions that often cause a problem for the would-be censors. In some states -- certainly not all -- the law that regulates materials that are obscene for minors has a specific exemption for libraries. State legislatures sometimes enact such exemptions for a variety of reasons, including a desire to keep the statute enforceable. That is, they don't want the law to wind up overturned by a court because it ran afoul of the strict protections of Free Speech that apply in libraries.
Not being a lawyer, I find it fairly difficult to rummage through state obscenity laws to see whether they've got library exceptions. I was pleasantly surprised when I found, entirely by accident, that Wisconsin state law was unusually clear on this point. Since it's unusually clear, I'll use it as an example.
Chapter 948 of Wisconsin state law defines what is obscene for minors, and imposes penalties for providing such materials to a minor. It also specifically exempts school and library staff from prosecution, and gives some reasons for doing so. Below is a portion of that law, which happens to be clear enough even for non-lawyers to get at least a partial understanding:
W.S.A. 948.1 Exposing a child to harmful material or harmful descriptions or narrations
. . . .
(4) Libraries and educational institutions. (a) The legislature finds that the libraries and educational institutions under par. (b) carry out the essential purpose of making available to all citizens a current, balanced collection of books, reference materials, periodicals, sound recordings and audiovisual materials that reflect the cultural diversity and pluralistic nature of American society. The legislature further finds that it is in the interest of the state to protect the financial resources of libraries and educational institutions from being expended in litigation and to permit these resources to be used to the greatest extent possible for fulfilling the essential purpose of libraries and educational institutions.
(b) No person who is an employee, a member of the board of directors or a trustee of any of the following is liable to prosecution for violation of this section for acts or omissions while in his or her capacity as an employee, a member of the board of directors or a trustee:
1. A public elementary or secondary school.
2. A private school, as defined in s. 115.001(3r).
3. Any school offering vocational, technical or adult education that:
a. Is a technical college, is a school approved by the educational approval board under s. 38.50, or is a school described in s. 38.50(1)(e) 6., 7. or 8.; and
b. Is exempt from taxation under section 501(c)(3) of the internal revenue code, as defined in s. 71.01(6).
4. Any institution of higher education that is accredited, as described in s. 39.30(1)(d), and is exempt from taxation under section 501(c)(3) of the internal revenue code, as defined in s. 71.01(6).
5. A library that receives funding from any unit of government.
You can look up Chapter 948 or any other Wisconsin State Law at:
http://www.legis.state.wi.us/rsb/stats.html
The library exemption is at 948.11(4).